Asymptotic Methods for Solitary Solutions and Compactons by Ji-Huan He

“…This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations. …”
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On the Approximate Analytical Solution to Non-Linear Oscillation Systems by Mahmoud Bayat, Iman Pakar

“…This study describes an analytical method to study two well-known systems of nonlinear oscillators. One of these systems deals with the strongly nonlinear vibrations of an elastically restrained beam with a lumped mass. …”
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Dynamics Evolution of Credit Risk Contagion in the CRT Market by Tingqiang Chen, Jianmin He, Qunyao Yin

“…This work introduces a nonlinear dynamics model of credit risk contagion in the credit risk transfer (CRT) market, which contains time delay, the contagion rate of credit risk, and nonlinear resistance. …”
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Chaotic Power System Stabilization Based on Novel Incommensurate Fractional-Order Linear Augmentation Controller by Abdul-Basset A. Al-Hussein, Fadhil Rahma Tahir, Karthikeyan Rajagopal

“…The nonlinear dynamics of an incommensurate fractional-order single-machine infinite-bus (SMIB) power system benchmark model are explored and studied by means of modern nonlinear analysis theories, such as bifurcation, chaos, power spectral density (PSD), and bicoherence methods. …”
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The Effects of Breathing Behaviour on Crack Growth of a Vibrating Beam by Wenguang Liu, Mark E. Barkey

“…Results indicate that not only does the stiffness oscillates during crack growth corresponding to the physically open and closed states of the crack, but also stiffness and friction damping oscillate nonlinearly with crack growth. This behaviour induces not only nonlinear dynamic response but also nonlinear crack growth. …”
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Suppression of Base Excitation of Rotors on Magnetic Bearings by Steven Marx, C. Nataraj

“…A four-degree-of-freedom model is used for the rotor system, and the bearings are modeled by nonlinear expressions. Each disturbance frequency is expected to produce a multiharmonic system response, a characteristic of nonlinear systems. …”
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APPLICATION OF CONVOLUTIONAL NEURAL NETWORK AND CHAOS THEORY IN FAULT DIAGNOSIS OF ROLLING BEARINGS by JIN JiangTao, XU ZiFei, LI Chun, MIAO WeiPao, ZHANG WanFu, LI Gen

“…In order to solve the traditional methods in the process of judging the fault type of the bearing caused by signal strongly nonlinear misjudgment wrongly, based on the chaos theory, the phase space reconstruction method（PSR） is used to restore the system dynamics characteristics and the convolution neural network（CNN） is used to learn and extract the effective nonlinear information from the chaotic sequence, proposes the PSR-CNN intelligent fault diagnosis method, visualizes the attractor trajectory, and analyzes the nonlinear characteristics of each fault signal. …”
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Topological phases and non-Hermitian topology in photonic artificial microstructures by Liu Hui, Lai Pengtao, Wang Haonan, Cheng Hua, Tian Jianguo, Chen Shuqi

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Holomorphic embedding method for large-scale reverse osmosis desalination optimization by Junzhi Chen, Tao Wang, Jiu Luo, Hongbo Chen, Yi Heng

“…Abstract Large-scale optimal design problems involving nonlinear differential equations are widely applied in modeling such as craft manufacturing, chemical engineering and energy engineering. …”
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An Inelastic Theoretical Model regarding the Load-Carrying Capacity of PSL Bending Component by Baolu Sheng, Yuling Bian, Dong He, Aiping Zhou

“…To predict the nonlinear bending performance of the PSL beams, a theoretical model that could consider the nonlinear stress-strain relations of PSL and predict the damage modes of the PSL beams was developed. …”
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Circuit Distortion Analysis Based on the Simplified Newton's Method by M. M. Gourary, S. G. Rusakov, S. L. Ulyanov, M. M. Zharov, B. J. Mulvaney

“…A new computational technique for distortion analysis of nonlinear circuits is presented. The new technique is applicable to the same class of circuits, namely, weakly nonlinear and time-varying circuits, as the periodic Volterra series. …”
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Approximate Solutions of Fractional Riccati Equations Using the Adomian Decomposition Method by Fei Wu, Lan-Lan Huang

“…The fractional derivative equation has extensively appeared in various applied nonlinear problems and methods for finding the model become a popular topic. …”
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Investigation of Factors Influencing the Structural Vibration in Ball Bearings by Kapil Mehra, Kambiz Farhang, Jayanta Datta

“…The lumped parameter formulation is obtained by treating various elements with mass lumped at their centers of gravity and the contact as nonlinear springs with nonlinear spring rates.…”
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Power Forecasting of Combined Heating and Cooling Systems Based on Chaotic Time Series by Liu Hai, Song Yong, Du Qingfu

“…Chaos is an inherent property of nonlinear dynamic system. A predicator of the output power of the distributed generation system is to establish a nonlinear model of the dynamic system based on real time series in the reconstructed phase space. …”
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Design of an Anti-Windup PID Algorithm for Differential Torque Steering Systems by Dengzhi Peng, Bin Huang, Hao Huang

“…Based on the built 8 DOF model, the vehicle performance indicators are calculated and compared, the gap between the models with linear and nonlinear tires is non-negligible, and a reference model with a nonlinear tire model is recommended for the relevant research. …”
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Displacement Transmissibility Characteristics of Harmonically Base Excited Damper Isolators with Mixed Viscous Damping by Xiaojuan Sun, Jianrun Zhang

“…Also, the influence of nonlinear damping on the response characteristics is investigated by comparing the transmissibility of linear and nonlinear systems. …”
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Multimodel Modeling and Predictive Control for Direct-Drive Wind Turbine with Permanent Magnet Synchronous Generator by Lei Wang, Tao Shen, Chen Chen

“…The desired trajectory of the nonlinear system is decomposed to be suitable for the reference trajectory of multiple models that are presented by the linear models of the nonlinear system, which simplifies the nonlinear optimization problems and decreases the calculation difficulty. …”
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Lump Solutions and Resonance Stripe Solitons to the (2+1)-Dimensional Sawada-Kotera Equation by Xian Li, Yao Wang, Meidan Chen, Biao Li

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Inclined Magnetic Field on Mixed Convection Darcy–Forchheimer Maxwell Nanofluid Flow Over a Permeable Stretching Sheet With Variable Thermal Conductivity: The Numerical Approach by Gossaye Aliy Adem, Adamu Gizachew Chanie

“…In order to analyze heat and mass transfer, the inquiry takes into account a number of variables, including the magnetic field, variable thermal conductivity, activation energy, suction/injection, and nonlinear thermal radiation. The controlling nonlinear PDEs with BCs are converted via similarity transformation into nonlinear ODEs in order to solve the ensuing nonlinear ODEs. …”
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Does Diversification Affect Banking Systemic Risk? by Shouwei Li

“…This paper contributes to the understanding of the linear and nonlinear causal linkage from diversification to banking systemic risk. …”
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